PERF EVAL CONTD H H There are many

PERF EVAL (CONT’D) H H There are many other “tools of the trade” used in performance evaluation Only a few will be mentioned here: – queueing theory – verification and validation – statistical analysis – multi-variate analysis – presentation of results 1

Queueing Theory H H A mathematical technique that specializes in the analysis of queues (e. g. , customer arrivals at a bank, jobs arriving at CPU, I/O requests arriving at a disk subsystem) General diagram: Customer Arrivals Buffer 2 Server Departures

Queueing Theory (cont’d) H The queueing system is characterized by: – Arrival process (M, G) – Service time (M, D, G) – Number of servers (1 to infinity) – Number of buffers (infinite or finite) H 8 H Example notation: M/M/1, M/D/1 Example notation: M/M/ , M/G/1/k 3

Queueing Theory (cont’d) H H H There are well-known mathematical results for the mean waiting time and the number of customers in the system for several simple queueing models E. g. , M/M/1, M/D/1, M/G/1 Example: M/M/1 – q = rho/ (1 - rho) where rho = lambda/mu < 1 4

Queueing Theory (cont’d) H H These simple models can be cascaded in series and in parallel to create arbitrarily large complicated queueing network models Two main types: – closed queueing network model (finite pop. ) – open queueing network model (infinite pop. ) H Software packages exist for solving these types of models to determine steady-state performance (e. g. , delay, throughput, util. ) 5

Verification and Validation H H H An important step in any modeling work (simulation or analytical) is convincing others that the model is “correct” Verification: develop simple test cases with known inputs; compare to expected outputs Validation: the “reality check” to see if model predictions agree with real world Sanity checks (e. g. , Little’s Law: N = T) This V&V process is often overlooked!!! 6

Statistical Analysis H H “Math and stats can be your friends!!!” CW There are lots of “standard” techniques from mathematics, probability, and statistics that are of immense value in performance work: – confidence intervals, null hypotheses, F-tests, T -tests, linear regression, least-squares fit, maximum likelihood estimation, correlation, time series analysis, transforms, Q-Q, EM. . . – working knowledge of commonly-observed statistical distributions 7

Multi-Variate Analysis H H For in-depth and really messy data analysis, there are multi-variate techniques that can be immensely helpful In many cases, good data visualization tools will tell you a lot (e. g. , plotting graphs), but in other cases you might try things like: – multi-variate regression: find out which parameters are relevant or not for curve fitting – ANOVA: analysis of variance can show the parameters with greatest impact on results 8

Presentation of Results H Graphs and tables are the two most common ways of illustrating and/or summarizing data – graphs can show you the trends – tables provide the details H H There are good ways and bad ways to do each of these Again, it is a bit of an “art”, but there are lots of good tips and guidelines as well 9

Table Tips H H H H Decide if a table is really needed; if so, should it be part of main paper, or just an appendix? Choose formatting software with which you are familiar; easy to import data, export tables Table caption goes at the top Clearly delineate rows and columns (lines) Logically organize rows and columns Report results to several significant digits Be consistent in formatting wherever possible 10

Graphing Tips H H H Choose a good software package, preferably one with which you are familiar, and one for which it is easy to import data, export graphs Title at top; caption below (informative) Labels on each axis, including units Logical step sizes along axes (10’s, 100’s…) Make sure choice of scale is clear for each axis (linear, log-log) Graph should start from origin (zero) unless there is a compelling reason not to do so 11

Graphing Tips (cont’d) H Make judicious choice of type of plot – scatter plot, line graph, bar chart, histogram H Make judicious choice of line types – solid, dashed, dotted, lines and points, colours H H H If multiple lines on a plot, then use a key, which should be well-placed and informative If graph is “well-behaved”, then organize the key to match the lines on the graph (try it!) Be consistent from one graph to the next wherever possible (size, scale, key, colours) 12